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We generalize two main theorems of matching polynomials of undirected simple graphs, namely, real-rootedness and the Heilmann-Lieb root bound.
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Young-Bin Choe, James G Oxley, Alan D Sokal, and David G Wagner, Homogeneous multivariate polynomials with the half-plane property , Advances in Applied Mathematics 32
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Petter Brändén, Polynomials with the half-plane property and matroid theory , Advances in Mathematics 216
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Maria Chudnovsky and Paul Seymour, The roots of the independence polynomial of a clawfree graph , Journal of Combinatorial Theory (May 2007), 350–357
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Alexander Engström, Inequalites on well-distrubted points sets on circles , Journal of Inequalities in Pure and Applied Mathematics 8
2007
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Julius Borcea and Petter Brändén, The lee-yang and pólya-schur programs. i. linear operators preserving stability , Inventiones mathematicae 177
2009
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Bodo Lass, Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs , Journal of Combinatorial Theory (2012), 411–423
2012
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2014
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Adam Marcus, Daniel Spielman, and Nikhil Srivastava, Interlacing families i: Bipartite ramanujan graphs of all degrees , Annals of Mathematics 182
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2015
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